


The Case of the Sunken Safe

by cnoocy



Category: Mathnet
Genre: Calculus, Codes & Ciphers, Combinatorics, Gen, Geometry, Mathematicians, Mathematics, Multiplication
Language: English
Status: Completed
Published: 2014-12-20
Updated: 2014-12-20
Packaged: 2018-03-02 08:48:31
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 5
Words: 7,257
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/2806601
Author URL: https://archiveofourown.org/users/cnoocy/pseuds/cnoocy
Summary: <blockquote class="userstuff">
              <p>A case brings Kate back to New York to help her new partner track down a theft. But unless Pat and George can help them solve the crime, it may be the last one of Kate's career.</p>
            </blockquote>





	1. Chapter 1

**Author's Note:**

  * For [kmo](https://archiveofourown.org/users/kmo/gifts).



> The story you're about to read is a fib, but it's short. Moderately short. The names are made up but the problems are real.

Monday, eight forty-five. New Yorkers were distracting themselves from worrying about the holidays by worrying about the Millennium Bug. I had prepared by having so many leftovers from Thanksgiving that I could live on them until February. My name is Tuesday. I'm a mathematician.

I picked up my messages from Sgt. Abruzzi on the way in and arrived at my office to find my partner, George Frankly, staring intently at a slot car track he had set up on his desk. And mine. 

"Are we starting a Mathnet division of Formula 1, George?" I asked, leaning over his shoulder.

George turned around, startled. "Pat! I was just thinking about calculus. See, as the cars go around the track, their position is constantly changing."

"And if we measure how fast that position is changing, that's what mathematicians call the derivative of the cars' position."

"And which is better known as their velocity. And if we measure how fast the velocity is changing, we get the derivative of the velocity..."

"Also known as their acceleration. So are you expecting us to solve a crime at the slot car races?"

"In this job, Pat? You never know!"

The door opened and our captain, Joe Greco, came in, looking puzzled. “You guys know anyone planning on a swim this weekend?” 

George looked at him, taken aback. "It's the middle of December, chief. That would be extremely dangerous! Why do you ask?"

"Because a Coast Guard patrol boat picked up someone in Long Island Sound this morning, and the one thing she said before collapsing was 'Mathnet'. She's down at Bellevue now. Go check it out."

"We're on it, chief." I nodded at George. "Let's roll, pard." We stood, checked our calculators, and left.

* * *

Our friend Benny Pill drove us uptown to Bellevue Hospital, where we were met by Dr. Jordan Santiago. We introduced ourselves and she took us to the room where our mysterious patient was being treated. "Does she look familiar to either of you?" she asked.

George and I shook our heads at each other. The woman in the bed was in her mid-to-late twenties, with wavy black hair, possibly South Asian. "We've never seen her before," I said. "Will she be all right?"

Dr. Santiago nodded cautiously. "We think so. She was very chilled, but she seems to be in good health generally, and there's no sign of brain damage. She probably won't be conscious until at least tomorrow, though."

"Could we see her personal effects?" asked George.

"The only thing she had other than the clothes she was wearing was this notebook, but it's in some sort of code." She handed us a small black notebook, which was still cold and slightly damp. I opened it, to find that it was full of numbers. "If you can use that to find out who she is, that would be very helpful."

* * *

We made copies of the notebook pages and took them back to the office. As George stowed his slot cars, I started looking at the first page of notes. I went to the board and wrote up the first few lines.

> 1=23
> 
> 16 * 11 22 21'1 * 1 15 16 21 18 * 1 15 12 * 23 19 8 21 * 16 26 * 1 22 * 26 1 12 8 19 * 1 15 12 * 26 18 16 11 26.  
> 

"Well, that certainly looks like a code for the alphabet, Pat." George said, looking up at the code as he put the slot cars down. "The numbers are in small groups, they're all between 1 and 26, and there's even punctuation."

"That's what I thought, but it's not simply mapping 1 to A, 2 to B, and so on, like some of the other codes we've dealt with. Look." I wrote the corresponding letter under each number: P KVU'A AOPUR AOL WSHU PZ AV ZALHS AOL ZRPKZ. "And what do you think that first line means?"

"One equals two to the third power? It might mean that whoever wrote this is bad at math! Heh-heh-heh. Two to the third power is eight."

I gave George a look. "Let's assume that whoever wrote this notebook, probably our mystery swimmer, is competent at math. What if that's the key to reading the message?"

"So when she writes that one is eight, she means to read the number eight as if it were the number one, which is the letter A! So to read the message, we subtract seven from each number before converting it into a letter." George picked up a piece of chalk and wrote the new numbers underneath my letters:

9 * 4 15 14'-6 * -6 8 9 14 11 * -6 8 5 * 16 12 1 14 * 9 19 * -6 15 * 19 -6 5 1 12 * -6 8 5 * 19 11 9 4 19.

"Let's add 26 to those negative numbers to bring them back into the range of letters, George." I changed the -6s to 20s, then wrote letters underneath:

I DON'T THINK THE PLAN IS TO STEAL THE SKIDS.

"'I don't think the plan is to steal the skids'," George read. "What are the skids? And why would she write that? If she's part of the plan, shouldn't she know what it is? And if she's not part of the plan, why is she writing about it?"

"Maybe because she's trying to stop it," I said, realization dawning gradually. "George, what if she didn't say 'Mathnet' to the Coast Guard because she was looking for us? What if she said 'Mathnet'..."

"Because she is Mathnet!" George finished my sentence with me. "But if she's Mathnet, which Mathnet department does she work for? And where's her partner?"

"Right here," said a voice from the door. The woman standing there was instantly familiar, even though we'd never met. I'd seen her picture on records from George's old cases, and even though she was wearing a darker suit and a more severe haircut, the cheekbones were unmistakable. "Hi, George," said Kate Monday. "How's Martha?"


	2. Chapter 2

Tuesday, eight fifteen. New Yorkers were waking up and getting to work, except for the ones who were already at work, the ones who worked nights and were going home to sleep, and the ones who had the day off and were sleeping in. I was envious of those last two as I fought the subway crowds. My name is Pat. I'm a mathematician.

We were working a case that had started with a mysterious stranger and now involved my partner's old partner. I decided to review some of the previous chapter to get my facts in order.

> Our captain, Joe Greco, came in, looking puzzled. “You guys know anyone planning on a swim this weekend?” 
> 
> George looked at him, taken aback. "It's the middle of December, chief. That would be extremely dangerous! Why do you ask?"
> 
> "Because a Coast Guard patrol boat picked up someone in the harbor this morning, and the one thing she said before collapsing was 'Mathnet'. She's down at Bellevue now. Go check it out."
> 
> ....
> 
> [Dr. Santiago] handed us a small black notebook, which was still cold and slightly damp. I opened it, to find that it was full of numbers.
> 
> ....
> 
> [I] wrote letters underneath:
> 
> I DON'T THINK THE PLAN IS TO STEAL THE SKIDS.
> 
> "'I don't think the plan is to steal the skids'," George read. "What are the skids? And why would she write that? If she's part of the plan, shouldn't she know what it is? And if she's not part of the plan, why is she writing about it?"
> 
> "Maybe because she's trying to stop it," I said, realization dawning gradually. "George, what if she didn't say 'Mathnet' to the Coast Guard because she was looking for us? What if she said 'Mathnet'..."
> 
> "Because she is Mathnet!" George finished my sentence with me. "But if she's Mathnet, which Mathnet department does she work for? And where's her partner?"
> 
> "Right here," said a voice from the door... "Hi, George," said Kate Monday. "How's Martha?"
> 
> [courtesy previous chapter]

I had hoped to get to the office before Kate, but she and I reached the office door at the same time. After a moment of confusion, I held the door for her. After I followed her into the office, I held out my hand to her. "I didn't get a chance to properly introduce myself at the end of the last chapter," I said. "I'm Pat Tuesday."

She shook my hand firmly. "Kate Monday, but I'm guessing you already know that. I'm with Mathnet Federal, usually attached to the FBI. My partner in the hospital is Samita Ravivara. Thank you for checking on her."

George got up from his chair to join us. "We're happy to, Kate. Can you help us make sense of her message here?"

Kate looked at the board, and then at the copied pages next to it. "Nice job figuring out our code. Let me fill out the rest of it." Working from the pages, she decoded the rest of the message in her head as she wrote it down:

> I don't think the plan is to steal the skids. I've been watching the weight when the truck goes through the scales, and it's wrong for the cargo. I think there's something else on the truck, and the thieves are going to steal that. I'll be watching to see if I'm right. 

"The skids are big bundles of paper, about three quarters of a ton each. We were helping with security for them, but apparently there was something else being shipped as well."

"Maybe it was something else more valuable than the paper," said George. "That's a lot of paper, but how valuable can paper be?"

"Pretty valuable, George. It was twenty-dollar bills, on their way from the Federal Reserve in Boston to the one here in New York."

"Wow! How much money is that?"

"It's a lot. Each skid is 40 cash-packs." Kate started putting numbers on the board. "Each cash-pack is 4 bricks, and each brick is 4 bundles.Each bundle is 10 straps, and each strap is 100 bills."

"So," I said, multiplying as she went, "each skid of twenties is worth one million two hundred eighty thousand dollars."

George whistled.

"Did the shipment arrive intact?" I added.

"That's a good question," said Kate. "Let's go ask."

* * *

We walked the seven blocks to the Federal Reserve Bank of New York. We were escorted to the office of a Junior Vice President for Currency Transfers named M. Vault, a man in his thirties with great hair and teeth. 

"Thank you for meeting with us, Mr. Vault," said Kate. "I'm Kate Monday, these are my associates..."

"Pat Tuesday, and my partner George,"

"Frankly,"

"Mathnet." We completed in unison, displaying our badges.

"Please sit," said Mr. Vault. "How can I help you all?"

Kate took the lead. "We're investigating a recent delivery of skids from Boston. It would have come in very early yesterday morning."

Mr. Vault consulted a computer on his desk. "It looks like there was a delay and it's being unloaded now. I can take you down there."

We went down to the secure loading dock. The truck was open, and the first skid was already out. We watched as a forklift driver drove back into the truck for the second skid.

"How much money was supposed to be on this truck?" George asked.

Mr. Vault checked his notepad. "The manifest says two million two hundred forty thousand dollars."

"That's short by a few hundred thousand!" I said. "There should be two million five hundred sixty thousand on two full skids of twenties."

Mr. Vault followed behind as we ran to watch the second skid come off the truck. Kate climbed up onto the skid, and nodded at me. "You're right, Pat. Look." I stepped up onto the side of the forklift to see. There was an empty space in the middle of the skid, surrounded by the stacks of bundled money.

"And see this!" shouted George from inside the truck. He was holding a jacket much like Kate's, and there was light shining down on him from a neatly cut hole in the truck's roof.

Kate hopped down from the skid and walked up to Mr. Vault. "Something other than cash was stolen from this truck," she said. "What was it?"

We returned to Mr. Vault's office and watched as he frantically consulted documents on his computer.

"Let me see," he said. "Yes, there was an additional item on that truck, but it's listed as secret. Let me get someone down here to clear it up." He picked up the phone and talked quickly into it. "Can you ask Ms. Knox to come down here, please?" He hung up and turned to us. "Ms. Knox is in charge of secret transactions here at the bank."

Ms. Knox arrived a few minutes later and got right to business. "The additional package on that shipment was a safe containing printing plates for new currency designs. If those plates have been taken by criminals, they could create counterfeit bills that are indistinguishable from genuine currency. Who was working on security for this shipment?"

Kate frowned. "That was us, Mathnet Federal, but–"

"Then you should probably figure out what happened and who has those plates!" Ms. Knox interrupted. "If they're actually in the hands of counterfeiters, you'll be lucky if all you lose is your job!"

Kate looked stricken as we were escorted from the building.


	3. Chapter 3

Wednesday, nine oh seven. New York was gray and rainy, commuters shuffling along the sidewalks and mumbling to themselves. I understood how they felt. Yesterday had been a disappointment, and I didn't have high hopes for today. My name is Pat. I'm a mathematician.

We were working on a case that had reunited my partner George with his old partner Kate, but now Kate was in trouble with the Federal Reserve. We decided to review some previous chapters to get our facts straight. It's good to make sure you have all the information when you're working on a problem.

>   
>  Our captain, Joe Greco, came in, looking puzzled. “You guys know anyone planning on a swim this weekend?” 
> 
> George looked at him, taken aback. "It's the middle of December, chief. That would be extremely dangerous! Why do you ask?"
> 
> "Because a Coast Guard patrol boat picked up someone in the harbor this morning, and the one thing she said before collapsing was 'Mathnet'. She's down at Bellevue now. Go check it out."
> 
> ....
> 
> "Because she is Mathnet!" George finished my sentence with me. "But if she's Mathnet, which Mathnet department does she work for? And where's her partner?"
> 
> "Right here," said a voice from the door... "Hi, George," said Kate Monday. "How's Martha?"
> 
> ....
> 
> Ms. Knox arrived a few minutes later and got right to business. "The additional package on that shipment was a safe containing printing plates for new currency designs. If those plates have been taken by criminals, they could create counterfeit bills that are indistinguishable from genuine currency. Who was working on security for this shipment?"
> 
> Kate frowned. "That was us, Mathnet Federal, but–"
> 
> "Then you should probably figure out what happened and who has those plates!" Ms. Knox interrupted. "If they're actually in the hands of counterfeiters, you'll be lucky if all you lose is your job!"
> 
> [courtesy previous chapters]

When I got to the station, everyone was discouraged, but Benny was waiting in the office to see Kate. "Now that's a sight for sore eyes!" he cried when she entered. "Kate, where have you been all this time?"

Kate smiled despite herself. "Remember the Strategic Weather Initiative case?" George and Benny nodded. "After that, the Polygon recruited me to do some work for them. But a year of working for them was plenty, and I jumped to the federal Mathnet office that was starting up. Since then I've been keeping busy, mostly working with the FBI. But not always; this current job is technically Secret Service. They called us up and asked us to help with this shipment of currency. They thought someone might want to rob it, so they had us figure out what resources someone would need to make off with the skids. But now this might be the last job for me."

"What do you mean, Kate?" asked Benny.

"Someone stole some currency plates from the shipment instead," said George. "Now Kate's on the hook to track them down, and we don't have much to go on." The phone rang, and he answered it. "Mathnet, Frankly speaking." He paused, then broke into a big grin. "That's great news. We'll be there in just a few minutes." He hung up. "Well, we should have more to go on shortly. Your partner's awake, Kate. Let's go see what she has to say."

* * *

Ms. Ravivara was sitting up in bed and having some tea when we arrived. She blinked a few times when we came in, then spoke to Kate. "I'm very sorry that I didn't report as scheduled upon my arrival in Manhattan, Ms. Monday."

Kate met her eyes very seriously for about ten seconds, then they both broke into laughter. "Don't give me that, Sam! I'm just glad you're alright." They hugged quickly, then Kate turned to introduce us. "This is my former partner George Frankly, his partner Pat Tuesday, and their undercover NYPD liaison, Benny Pill." We leaned in to shake hands, then retreated. "Now, how did you get from traveling with a shipment of money to swimming in the ocean?"

Sam shivered at the memory. "I was thinking about someone trying to steal the skids, and watching the scales at the highway weigh stations. We ran all those different scenarios, from breaking the skids apart to stealing the entire truck, so I knew exactly how much the truck weighed with and without the money on it. The weight of the truck was off. The driver thought I was just being paranoid, but he let me keep watch in the back. When I heard the helicopter coming, I hid." 

"But we made sure no large helicopters were available anywhere along the route." 

"They didn't need a large helicopter. They had a small target, so they used a small helicopter. They cut a hole in the roof, attached a line to a safe hidden in the middle of the skid, and took off." 

"So how did that get you into the water?" asked George.

"Sam, you didn't!" gasped Kate.

"I didn't know what else to do!" Sam shrugged at Kate. "When the safe started moving, I jumped on. I'm not even sure they knew I was on there. I'm sure that they figured it out about half an hour later, though."

"What happened half an hour later?" I asked.

"Well, when I found myself riding a stolen safe through the sky, I wasn't sure what to do. I was way too high to jump off, and I didn't want to lose the safe. But after thirty minutes or so, we passed over the water. I figured I wasn't going to get a better chance, so I said a quick prayer and cut the line. The helicopter went up and I followed the safe down, and that's all I remember until about an hour ago." 

"The Coast Guard picked you up," I told her. "You said 'Mathnet' to them before passing out, which is how George and I got involved."

"So what's the status of the case, then?" Sam asked.

We all looked to Kate. She took a deep breath and began. "Well, let's see. The safe, as it turns out, contained printing plates for currency, which is a literal gold mine for counterfeiters. We've determined that the plates were stolen, but the thieves probably haven't recovered them yet. The Federal Reserve is blaming us for allowing the theft, so we need to figure out who actually took them. And if it's at all possible, we need to recover that safe ourselves."

"First things first, then," said Benny. "Sam, let's see if we can get you out of here and back to the office."

* * *

Sam's doctors were willing to release her as long as she promised to stay warm and not do any more swimming, so we regrouped in the office with some takeout. We decided to start with the helicopter.

"Sam," asked Kate, "what do you remember about the helicopter? Did you see its size, or any of its identification number?"

Sam thought for a minute. "It was small, and white. I could see the number, but not well. There was an N, then either a 3 or an 8 or a B, then a 1 or I, then two more 3-8-B's, then a 4 or an A."

"That's three times two times three times three times two." I wrote each set of possible signs on the board. "One hundred and eight possibilities."

"But those might not all be possible numbers," said Benny.

"What do you mean?" asked George.

"If helicopter numbers are at all like license plates, then there's rules about what parts are numbers and what parts are letters. So if we find out what those rules are, maybe we can cut down on our options."

"That sounds good. Let me see if I can track those down." Kate picked up the phone.

"You need to dial 8 to get an outside line now," I told her. "They put in a new system two years ago."

"Thanks," she said, and dialed. 

"We had a case this summer tracking down a prankster who was flying remote control planes around national monuments," Sam said quietly as Kate talked on the phone. "By the time it was over, we both had the number for the Federal Aviation Administration memorized."

Kate said "Thanks again, Judy," and hung up. She picked up the notes she had made while talking. "Okay, here are the rules. An N-Number, an identification number starting with N, can be one to five numbers, one to four numbers followed by one letter, or one to three numbers followed by two letters. They can't have a zero as the first number, and they can't contain the letters I or O."

"So the second number has to be a one," said George. I crossed out the I.

"And only the last two can be letters," added Sam. I crossed out the first two Bs.

"And the next-to-last can only be a letter if the last one is also a letter," I said. I circled the last two groups, and wrote a list of possibilities beneath them: 34, 84, 3A, 8A, BA.

"So now we have two times two times five possible numbers," said Kate. "Just twenty. That's a lot better than one hundred and eight."

"Can you call Judy back and get a twenty for our twenty? Heh-heh-heh." George chuckled. "You know, a location. Like on a CB."

Kate gave him a look. "Uh-huh." I sent her a sympathetic glance. She called back and spoke with Judy again. "Judy, I've got a partial number for you. Yes, an N-number. Three or eight, one, three or eight, and then one of the following 5 pairs. Ready?" She paused a moment. "Okay. Thirty-four, eighty-four, three-A, eight-A, or B-A. Yes, a helicopter, probably a one or two-seater. Can you fax it to Mathnet at the NYPD? Thanks. Yes, I owe you one. Talk to you soon." She hung up. "She's going to look it up and send us what she finds."

We continued eating, thinking about the case. Not too much later, Sgt. Abruzzi stopped in with a sheet of paper. We thanked him and sent him on his way with a spring roll, then clipped the page to the board. "N313BA," Benny read aloud."A Robinson R22 owned by Queens Helicopter Rentals. Should we go see what they can tell us?"

The four Mathnetters in the room looked up. "Let's roll!" we said in unison.

* * *

Queens Helicopter Rental was on 31st Ave, across Flushing Bay from LaGuardia Airport. We arrived there late in the day, as the office was getting ready to close, but the owner, Sasha Kasparov, was happy to speak to us. George and I introduced ourselves as Kate and Sam looked around. 

"We're trying to track down who may have rented a Robinson R22, number N313BA, over the weekend and into Monday," George asked. "Can you tell us who that was?"

"You have read my mind!" said Mr. Kasparov. "I was just about to call you about this helicopter."

George and I looked at each other, baffled. "You were?" I asked.

"Yes, yes! On Friday, a man came to my office. He asked to rent a small helicopter, which he would fly, and he wanted to pay cash. I was suspicious, but he was paying very well, and I don't get a lot of winter business. So I rented him the bird for the weekend, but I decided I would ask him for real identification when he returned it on Monday."

"So did you get his name off his ID then?" I asked.

"No, because he never showed up! He flew off with my helicopter, and it's still gone!"


	4. Chapter 4

Thursday, eight thirty-eight. New York was windy and bright. The morning commuters running down the sidewalks held their hands above their eyes as if they were looking for something missing. I certainly was. My name is Pat. I'm a mathematician.

We were already missing some currency plates belonging to the U.S. government, but as of yesterday, we were also missing a small helicopter belonging to a businessman from Queens. It was a pickle, and we decided to review some scenes from previous chapters to look for things we missed. When a problem gets more complicated as you work on it, it's good to take another look at your data in case there are hidden connections that can help simplify things.

> Sam shivered at the memory. "I was thinking about someone trying to steal the skids, and watching the scales at the highway weigh stations. We ran all those different scenarios, from breaking the skids apart to stealing the entire truck, so I knew exactly how much the truck weighed with and without the money on it. The weight of the truck was off. The driver thought I was just being paranoid, but he let me keep watch in the back. When I heard the helicopter coming, I hid." 
> 
> "But we made sure no large helicopters were available anywhere along the route." 
> 
> "They didn't need a large helicopter. They had a small target, so they used a small helicopter. They cut a hole in the roof, attached a line to a safe hidden in the middle of the skid, and took off." 
> 
> ....
> 
> "You have read my mind!" said Mr. Kasparov. "I was just about to call you about this helicopter."
> 
> George and I looked at each other, baffled. "You were?" I asked.
> 
> "Yes, yes! On Friday, a man came to my office. He asked to rent a small helicopter, which he would fly, and he wanted to pay cash. I was suspicious, but he was paying very well, and I don't get a lot of winter business. So I rented him the bird for the weekend, but I decided I would ask him for real identification when he returned it on Monday."
> 
> "So did you get his name off his ID then?" I asked.
> 
> "No, because he never showed up! He flew off with my helicopter, and it's still gone!"
> 
> [courtesy previous chapters]

I got to the office before George for once. Sam was there already, and I made sure to get her a hot coffee to support her continuing recovery. "Sam, I've been thinking about your trip through the air. Do you think you could identify where you started, and which way you were going?"

"I could, Pat, if only I knew the area. I've never spent much time in this area, so even though I know what landmarks I saw, I can't find them on a map."

"Well, I've been in the area for eight years. Maybe I can help with locations based on your descriptions. Where did you start?"

"We were traveling down a heavily wooded highway, not a rural road, but an actual highway. It had just gone from having lots of shops to nearly deserted when I moved to the cargo area of the truck."

"That sounds like Route 15 through Connecticut. Did you see the area at all when you left the truck on the safe?"

"No, but it was just after a long tunnel. It took us more than 10 seconds to pass through."

"The West Rock Tunnel!" I knew exactly where the truck had been when the helicopter left it. I got a map of the Long Island Sound from the shelf and put it up on the wall. I placed a pin on the location, just to the north-northwest of New Haven. "And did you see any landmarks to let you know which way they were headed?"

Sam put her coffee down and jumped slightly. "I did! The helicopter made a beeline for the shore, and I passed directly over a tall octagonal tower. It was so close, I probably could have just dropped the safe and myself on the balcony if I had been a little more alert."

"Was it a white stone octagonal tower, with a round iron top?"

"Yes."

"The Five Mile Point Lighthouse in New Haven." I put another pin on the location, at the southern end of New Haven Harbor. "Was the helicopter turning at all?"

"No. It was an almost windless day, too. The flags were all still, and they were traveling very straight, accelerating as they went."

I grabbed a ruler and drew a line across the sound as Kate and George came in. "Good morning, folks," George said. "Been doing some morning orienteering?"

"Yes, we have," I said. "Want to go out to Long Island and see who's seen our helicopter?"

* * *

It took about two hours to get out to the Riverhead area, and we filled Kate, George, and Benny in on the way. We arrived in Riverhead in the mid-morning and started asking around. We found a retired gardener named Peter Watering in a local restaurant having an early lunch. We introduced ourselves and asked whether he'd seen an unfamilar helicopter anywhere around.

"As a matter of fact, I did. This would have been very early Monday morning, around sunrise?"

"Yes," said Sam, "just after sunrise."

"I was walking on the beach, and I saw a small white helicopter come over off the sound. I think it landed over by the country club, if you want to go ask them."

"Can you give us directions?" asked Kate.

* * *

At the country club, we were met by a receptionist named Leopold Silver. "Good day, and welcome to the Oaks," he said. "How may I assist you?"

"Hello," said Sam. "My name is Sam Ravivara, and this is my partner Kate,"

"Monday," continued Kate as they showed their badges. "Mathnet. We'd like to look for a helicopter that may have landed here on Monday morning."

"I'd love to help you, but I'm afraid we have a policy of requiring a full police officer for any non-members to range about on the grounds."

"Will this do?" asked Benny, displaying his badge.

"Oh, that will do nicely," said Mr. Silver. "Would you like a couple of golf carts to get around the property?"

We spent some time wandering the grounds looking for any sign of a helicopter. We were about to give up when we found a set of stables at the edge of the property. "Sam," said George, "Do you think the helicopter could fit in there?" We approached carefully. Horses grumbled at the cold wind. George grabbed a crate and looked in a high window. "I see horses in stalls. Horse, horse, horse, horse, long flat blade sticking out of the stall." He turned and grinned at us. "I think that's a helicopter."

As Benny made arrangements for the helicopter to be collected and delivered to the NYPD impound lot, we returned to Mr. Silver and asked about the stables. "Those actually belong to an adjoining farm," said, "but members at the Patron level and above have access to them."

"Can we see a list of Patron members who were on the property on Monday?" Kate asked.

"Certainly. This is our sign-in book." He placed a large tome in front of us, and turned to Monday's page.

We scanned the names eagerly. It didn't take us long. "Leopold," I asked, "is this Marcus T. Vault a banker by any chance?"

"I believe he is. I think he works for a government bank in the city."

"That's M. Vault from the Federal Reserve. He must be hoping to sell the plates."

"He'll be hard to catch," said Kate. "We can probably prove he took the helicopter, but keeping a rental helicopter for a few extra days would just be a fine. We need to find a way to prove that this helicopter stole the safe, and the good evidence is somewhere at the bottom of Long Island Sound."

"So we know who our culprit is," exclaimed Sam, "but we have a near-impossible task to prove it was them! This is just like Sioux Falls all over again!"

George and I exchanged a look and mouthed "Sioux Falls?" to each other.


	5. Chapter 5

Friday, eight fifty-seven. New York was coated with a light dusting of snow, and it made the city beautiful, if only for a short time before the snow melted or turned to slush. The sight filled me with confidence, and I began to think that this case could actually be solved. My name is Pat. I'm a mathematician.

We were working a case where we had solved the crime, identified the culprit, and knew where the evidence was, but we weren't sure we'd be able to consider it a success. I decided to review some of the facts to see if I'd missed anything. Sometimes taking a fresh look at things can reveal information that's crucial to solving a problem.

> I grabbed a ruler and drew a line across the sound as Kate and George came in. "Good morning, folks," George said. "Been doing some morning orienteering?"
> 
> "Yes, we have," I said. "Want to go out to Long Island and see who's seen our helicopter?"
> 
> ....
> 
> "I was walking on the beach, and I saw a small white helicopter come over off the sound. I think it landed over by the country club, if you want to go ask them."
> 
> "Can you give us directions?" asked Kate.
> 
> ....
> 
> George grabbed a crate and looked in a high window. "I see horses in stalls. Horse, horse, horse, horse, long flat blade sticking out of the stall." He turned and grinned at us. "I think that's a helicopter."
> 
> ....
> 
> "That's M. Vault from the Federal Reserve. He must be hoping to sell the plates."
> 
> "He'll be hard to catch," said Kate. "We can probably prove he took the helicopter, but keeping a rental helicopter for a few extra days would just be a fine. We need to find a way to prove that this helicopter stole the safe, and the good evidence is somewhere at the bottom of Long Island Sound."
> 
> "So we know who our culprit is," exclaimed Sam, "but we have a near-impossible task to prove it was them! This is just like Sioux Falls all over again!"
> 
> George and I exchanged a look and mouthed "Sioux Falls?" to each other.
> 
> [courtesy previous chapters]

We met at the NYPD impound lot, where we gathered around the helicopter, still perched on the flatbed that had brought it here from Long Island. "Well, let's take a look," said Kate, and climbed inside. "There's some sort of electronic device attached to the console. I think it might be some sort of tracking system." She carefully detached it from the copter and handed it to Sam before leaning over to look in the small area behind the seats. "And the cable's still back here. Looks like heavy sailing line. Did you cut this with your pocket knife, Sam?"

"Yes. I think it split easily because it was under tension. I lost my knife in the water, though. Is it distinct enough to match with the other side, do you think?"

"I think so. Look." Kate held up a chaotically frayed rope end. "Now we just need to find the other end. Let's take this back to the office and try to get some data off of it."

* * *

Back at the office, we had the computer analysis department pull the data and give us a printout. We put the printout down in the middle of the table and gathered around it.

"So, here's the log for Monday morning," I said, pointing out the last few entries on the page. "We have time, speed acceleration, and altitude. At the beginning of the day, there's a short trip followed by a very short stop. I think that's the helicopter landing on the truck."

"I agree," said Sam. "That's the right time of day."

"And then they take off, then accelerate slowly for the next thirty-three minutes, up to sixty miles per hour," said Kate. "That matches what Sam reported."

"At the end of which there's a sudden jump in altitude when I cut the cable." Sam pointed. "That's one small step in altitude for a helicopter, and one giant leap of faith for a Mathnetter!"

We laughed. Kate patted Sam on the back.

"Good," George said, "but that doesn't tell us where they were when the cable was cut. This doesn't have coordinates for the helicopter at any of these points."

Realization struck me. "George, your slot cars! From Chapter 1!"

"I don't remember any slot cars in Chapter 1," said Kate. "But I only came in at the very end."

"Don't look at me," said Sam. "I spent that chapter unconscious, remember?"

"When I got in that morning, George had some slot cars set up," I explained. "He was using them to think about calculus, how position is related to speed and to acceleration."

"And now we have the acceleration of the helicopter, and we're trying to find the position!" Sam was starting to get excited as the impossible task began to look possible. She went to the board and drew a graph, a straight diagonal line from zero on the left side to the top right corner of the graph. She labeled the vertical axis of the graph "Speed: miles/hour" with a data point at 62. Then she labeled the horizontal axis "Time: hours" with a data point at 33 minutes, which she then converted to 33/60 hours, then simplified to 11/20, then to 0.55.

"We're trying to find out how many miles they traveled," said George, "and hours multiplied by miles per hour is miles. We want the area of this graph." Sam shaded the area under the line.

"And the area of a triangle is the base times the height divided by two." I pulled out my calculator. "Sixty-two times point five five divided by two is... seventeen point oh five miles from the beginning of the trip." 

Sam wrote the number on the board. "We know where the safe is. Now we just need to fetch it from the bottom of Long Island Sound."

"Would you believe Pat and I have experience with this?" asked George. "We fetched a stolen diamond from the bottom of Monterey Bay a few years ago. I'll call up MBARI and see if they know someone local who can help." He picked up the phone and dialed. "Yes, this is George Frankly from Mathnet in New York. Oh, it's nice to talk to you, too! Say, we're trying to recover something from the bottom of Long Island Sound. Yes, in December. That's why I was wondering if you knew of any Remote Operated Vehicles in this area. Hooey? Oh, W-H-O-I. Woods Hole Oceanographic Institute? I'll give them a call." He hung up. "I'm going to call WHOI and see what they can do for us."

WHOI is on Cape Cod, past the other end of the sound, so we arranged to take a police boat to meet their research vessel in the middle of the sound. As we stepped on board, we were met by a cheerful woman in her thirties with a long braid. "Hi!" she said. "I'm Avon Russell, a doctoral student at MIT working with WHOI. Come belowdecks and we'll get set up."

We introduced ourselves. We were starting to get the hang of the four-person introduction. "We worked with MBARI on a somewhat similar case a few years ago," George said. "We were only recovering a cummerbund that time, though. Will the ROV be able to pick up a small safe?"

Ms. Russell nodded. "I saw Dr. Jeong give a talk about it at an oceanography conference. We'll be using Jason, an ROV designed for deep oceanfloor work. It has an 'elevator' platform that it can place heavy items on for lifting by the ship's winches. Do you know where the safe is?"

"We think so," said Sam, "but we haven't seen it on the seafloor. It was hanging from a helicopter, and I cut the cable. We were 100 feet up and traveling 62 miles an hour at the time."

"You will have to tell me more about that story later," said Ms. Russell. "For now, do you have detailed location information?" Kate pulled out our various logs and calculations. Ms. Russell called the ship captain over, and they conferred over the map as she looked up some additional information on a laptop computer. "I'm pulling up the currents and tidal information for the time that the safe was sinking, so we can figure out where it would have come to rest after hitting the water." She circled a spot on the map and showed it to the captain, then proceeded to the back of the room, where a pilot was set up with screens showing the surface of the sound. "This is the ROV control area," she said. "We were already doing a training exercise in the sound, so your timing is very good. In a week, this ROV will be getting pictures of benthic organisms at the bottom of the North Atlantic." The ship moved to get into position, and the ROV dropped into the water. "We're only going down a few dozen meters today, but the tether connecting Jason to its surface unit Medea is 6 miles long." We watched marine animals and sadly, some trash pass by as the machine descended. Finally, we saw the seafloor, and a dark shape sitting partially embedded in it.

"That's it!" said Sam. "See, it still has the cable wrapped around it!"

We watched as the pilot had the ROV carefully lift the safe and place it on the elevator platform. Then we rushed outside to see the safe arrive on the ship. We all held our breath as the platform was lowered onto the deck. Kate walked up to the safe and pulled the end of a long rope out of a satchel. The ends matched perfectly. 

George had already dialed his phone. "It's a match, Benny," he said. "Move in on Mr. Vault." He gave us all a thumbs-up, and we high-fived in celebration.

**Author's Note:**

> M. T. Vault was charged with a 641, theft of government property, and a 471, conspiracy to commit counterfeiting. He was tried in New York City for the federal government and is now spending many years far away from the Federal Reserve System.


End file.
